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University of Florida | Journal of U ndergraduate Research | Volume 13 Issue 2 | Spring 201 2 1 Andrew Buckspa n College of Engineering University of Florida Wind power is a rapidly growing source of alternative energy that presents numerous control problems. One of these problems i s that the turbine dynamics are nonlinear and contain states that are difficult or not possible to measure. A control strategy is developed in this study to track a desired angular velocity despite uncertainties in the dynamics. The control scheme uses a dynamic neural network to identi fy unknown parameters and a neural network feedforward controller augmented by a robust integral of the sign of the error (RISE) feedback term. Performance is verified through numerical simulations. INTRODUCTION Wind energy is presently one of the faste st growing sources of alternative energy, providing a clean, emission free alternative to fossil fuels. In the last two years, total worldwide installed capacity has exceeded 150 GW . Additionally, the United States Department of Energy has proposed a comprehensive plan for wind energy to provide 20% of U.S. electrical energy by 2030 . Wind turbines are classified as either horizontal wind turbines (HAWTs) or vertical axis wind turbines (VAWTs). While VAWTs are able to more efficiently capture power from wind that frequently shifts directions, HAWTs are typically used for large scale turbines . HAWTs have an advantage in that the entire rotor assembly is placed high above the ground, where wind speeds are typic ally faster. Additionally, VAWTs exper ience higher mechanical stresses due to the asymmetry of the forces exerted on the blades . These attributes have led HAWTs to become the industry standard configuration and is the configuration considered in this study Generally, three regions of ope ration are identified based on wind speed and mechanical properties of a specific turbine . In Region I, the wind speed is below a minimum level required to overcome mechanical and electrical losses in the turbine, and the turbine is not allowed to oper ate. In Region II, the wind speed is above minimum, but it is not high e nough to cause the turbine to operate above its maximum rated capacity. In Region II, control can be achieved by applying a brake torque to the turbine drive shaft to achieve a desired rotational velocity At the higher end of Region II, this brake torque can saturate, in which case the rotor blades are tilted to maintain the desired rotational velocity. In this study it is assumed that the wind velocity is not high enough to cause sat uration of the brake torque, so control of the blade pitch angle is not considered. In Region III, the wind speed is above a maximum rated speed, and the rotor blades are pitched to she d excess power. Since wind turbines usually operate in Region II, this region will be considered in this study Control in Region II is significantly complicated by the fact th at the turbine dynamics are non linear and include unknown and unmeasurable terms. These unmeasurable terms include the torque exerted on the turbine by the wind the power captured by the turbine at the blades and the coefficient of performance of the turbine A number of control strategies have been proposed to deal with these problems. One approach  involves linear ization of the turbine dynamics, a nd the application of a typical PID controller ; however, the linear assumption can lead to reduced performance and reliability. An improvement on the linearized PID method is sliding mode control . This method provides better tracking of a desired rotat ional velocity than controllers developed for linear dynamics However, sliding mode control methods, such as , assume that the power captured by the turbine is measurable, which is generally not the case. In , the approach use d to compensate for th e nonlinear dynamics is an adaptive control algorithm. However, the controller in  is developed under the assum ption that the power captured by the turbine can be measured based on the electrical power generated by the turbine. This is not the case in p ractice as there exists variable loss in the conversion of mechanical energy captured at the blades to electrical energy out of the generator. In [ 3 ], a feedback controller is presented for a specific turbine. While this controller achieves good r esults, it assumes a priori knowledge of optimum values for the unknown turbine parameters. However, these values are specific to the turbine the control ler is implemented on and realistically change based on turbine geometry and mechanical parameters. This appr oach is therefore difficult to adapt to new turbines. Methods for estimating the unknown parameters have been proposed. One such method, given in [ 8 ], uses a least squares Kalman filter to estimate the unknown aerodynamic torque. Again, this method assumes optimum values for unknown turbine parameters are known.
ANDREW BUCKSPAN University of Florida | Journal of U ndergraduate Research | Volume 13 Issue 2 | Spring 201 2 2 The most relevant work to t he controller developed in this study is found in  and . In [ 9 ], a robust control strategy was used to estimate the unknown coefficient of performance and track a d esired trajectory However, this controller was shown to converge very slowly. A robust controller was also developed in [ 10 ] and was combined with a numerical extremum seeking algorithm to estimate the unknown coefficient of performance However, this nu merical method is prone to instability and possibly large estimation error. This study builds upon the control strategies developed in  and  by using a robust integral of the sign of the error (RISE) feedback term along with a dynamic neural network feedforward term in the controller. Additionally, the dynamic neural network is used to estimate the unknown coefficient of performance. This study focuses on developing a controller that can track a desired turbine rotational speed despite the un observab le coefficient of performance term A control ler dev eloped in [ 1 1 ] uses a robust control scheme with a multi layer neural network to track a desired trajectory despite nonlinear system uncertainties This study will focus on adapting the control strategy d eveloped in [ 11] for use in a wind turbine. DYNAMICS The wind turbine blades are characterized by two controllable parameters. One parameter is the tip speed the turbine blades to the wind spe ed. The tip speed ratio is defined as (1 ) where (t ) i s the rotational speed of the turbine blades, R is the radius of the circle swept by the blades, and v (t) is the wind speed. These quantities are all assumed to be known or measurable, and hence t he tip speed ratio is measurable. The tip speed ratio can be directly controlled by controlling the rotational speed of the turbine, which will be discussed. The second of controllable parameter is the blade pitch angle, For simplicity, the subsequent a nalysis assumes that each of the turbine blades is pitched to the same angle. Furthermore, the blade pitch angle will not be controlled, so the pitch angle for each blade will be considered constant. The overall p erformance of the turbine can be characteri zed by the coefficient of performance, C p which is a function of both tip speed ratio and blade pitch, and is defined as the ratio of the power captured by the turbine to the power available in the wind. The coefficient of performance can be expressed as (2) The captured power is not considered measurable; hence, C p is not considered measurable. The power available can be expressed as (3) and A is the area swept by the turbine blades. These parameters are known and time invariant ; hence the available power is a known and measurable quantity. Inserting (3) into (2) and rearranging gives an expression for the captured power as (4) The open loop turbine dynamics are given by the first order differential equat ion (5) where J is the total inertia of the system, C D is the total viscous damping in the system, and c (t) is the control torque exerted on the turbine drive shaft, which are all known or measurable terms. Also in (5), aero (t) is the aerodynamic torque exe rted by the wind on the turbine and can be expressed as (6) Combining (6) with ( 3) and (1), and rearranging gives (7) It is clear from (7) that estimating C p allows aero (t) t o be estimated CONTROLLER DESIG N The control objective is to design a controller that can track a desired trajectory, d (t), despite terms in the dynamics that are considered unknown where (t) is considered a controllable quantity. To this end, control can be achieved by applying a brake torque, c (t) to the turbine drive shaft to achieve a desired rotational speed.
N ONLINEAR C ONTROL OF A W IND T URBINE University of Florida | Journal of U ndergraduate Research | Volume 13 Issue 2 | Spring 201 2 3 To quantify this objective, a tracking error is defined as (8 ) where the desired trajectory and its derivatives are known and considered bounded. To facilitate further analysis, a filter ed tracking error is defined a s (9 ) where is a known scalar. This filtered tr acking error is not measurable because it depends on which is not a measurable quantity. Premultiplying ( 9 ) by J the open loop error system becomes (10 ) where f d (t) is an auxiliary function. The universal approximatio n theorem can be used to approximate f d (t) using a three layer neural network with five hidden nodes given a s (11 ) where W V 1 V 2 are bounded constant ideal weight matrices, () is an activation function, and ( ) is a reconstruction error In this study () is chosen to be a sigmoid function. The controller can be designed using a three layer neural network feedforward term augmented by a RISE feedback term a s (12 ) where the RISE feedback term (t) is given as [ 1 2 ] (13 ) and k s and 1 are positive, constant control gains. The estimates for the ideal neural network weights are generated on line as (14 ) (15 ) (16 ) where , are positive definite, constant symmetric control gain matrices. Here, () denotes the partial derivative of Additionally, a dynamic neural network identifier is used to genera te an estimate for and is given by (17 ) where k SIMULATION AND RESUL TS Using the controller designed in (1 2 ) and identifier designed in (1 7 ), a simulation was perfor me d in SIMULINK. The simulation parameters are shown in Table 1 The wind turbine mechanical parameters are based on the parameters of the three bladed Controls Advanced Research Turbine (CART 3 ), located at the National Wind Technology Center (NWTC ) The desir ed trajectory was selected from [7 ] as (18 ) which is appropriate for turbines operating in Region II. A simple model for gusting wind is given in [1 3 ], where the velocity is given by (19 ) where v m is the mean wind velocity of 5 m/s and v g (t) is the gust velocity, modeled as ( 20 ) The controller and identifie r gains were selected as shown in Table 2. I 6 x 6 denotes the identity matrix of size 6 by 6
ANDREW BUCKSPAN University of Florida | Journal of U ndergraduate Research | Volume 13 Issue 2 | Spring 201 2 4 k s 7,500,000 5 1 70 0.00 00 1I 6x6 70,000 0.25 k 5 10 Figure 1 below shows the tracking error as a function of time. The initial rotational velocity is started far away from the DC value of the desired rotational velocity, which accounts for the large initial value of the error. There is a slight amount of overshoot as the actual rotational velocity converges to the desired rotational velocity, causing an overshoot of around 5%. Figure 2 shows the actual rotational velocity and the desired trajectory t ogether. The large initial error can be seen to be caused by the initial conditions. The transient be seen to die out very quickly, and the actual rotational velocity perfectly tracks the desired rotational velocity. This is an interesting result, as even though some of the turbine dynamics were considered unobservable, the control system was able to converge to the desired trajectory relatively quickly, and stayed there with no steady state error. Figure 1 Controller tracking error as a function of time for the first seven seconds of the simulation. Figure 2 Actual turbine rotor speed versus desired rotor speed. C onvergence happens very quickly, and there is zero steady state error. CONCLUSION AND FUTUR E WORK The developed method derived from  is able to estimate the unknown and unmeasurable coefficient of performance in the plant dynamics and track a desired trajectory. This control strategy was successfully adapted to a wind turbine. The combined neural netwo rk and RISE control scheme is able to track a continuous, time varying desired rotational speed. The ability of this control strategy to handle nonlinear and unknown terms in the turbine dynamics was verified using a simplified computer simulation. Th e si mulation used to analyze the performance of the control system was based on a first principles model using turbine. NREL has a more complex simulation environment, known as the Fatigue, Aerodynamics, Structure s, and Turbulence (FAST) code. An area of future work is to further investigate the performance of this control ler using the FAST code. For example, the combined RISE/neural network controller can be simulated using complicated, stochastic wind fields. Als o, the desired reference rotor speed could potentially be a more complicated trajectory. Instead of a simple sinusoid, this trajectory could be generated to guarantee optimal power capture given the current wind conditions.
N ONLINEAR C ONTROL OF A W IND T URBINE University of Florida | Journal of U ndergraduate Research | Volume 13 Issue 2 | Spring 201 2 5 REFERENCES  World Wind E nergy Association. (2010, March 10) World Wind Energy Report 2009 [Online]. Available: http://www.wwindea.org/ home/index.php?option=com_content&task =view&id=266&Itemid=2  U.S. DOE Office of Energy Efficiency and Renewable Energy (2008, July) 20% wind energy by 2030 [Online]. Available: http://www1.eere.energy.gov/windandhydro/pdfs/41869.pdf  American Control Conf. St. Louis, MO, 2009, pp. 2076 2089. Litton Educational Publishing Inc New York, 1981. Industri al Applications Conf. San Diego, CA, 1996, pp. 1613 1618.  B. Beltran, T. Ahmed Power Control of Variable IEEE Trans. Energy Convers., vol. 23, no. 2, pp. 551 558, 2006. J. of Wind Eng. and Industrial Aerodynamics vol. 85 no. 3 pp. 293 308 April 2000. ol Ph.D. dissertation, Technical Univ. of Denmark, Copenhagen, Denmark 1997 o maximize American Control Conf. Seattle, WA, 2008, pp. 1824 1829. .S. thesis Dept. Mech. Eng., Kansa s State Univ., Manhattan, 2010. uncertain dynamic systems via a multilayer neural network feedforward and I EEE Trans. Autom. Control vol. 53 no. 9, pp. 2180 2185, 2008. IEEE Trans. Control Syst. Technol ., vol. 16, no. 2, pp. 373 379, 2008.  model for representing variable speed wind turbines in power system IEEE Trans. Power Syst. vol. 16, no.1, pp. 144 151, 20 03.